Question

48. A borrower makes a fully amortizing $100,000 loan at 3 percent for 30 years. The borrower is considering paying off the loan after 15 years. How much is the borrower saving in interests by paying off the loan earlier?

Answer 1

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

100000= Cash Flow*((1-(1+ 3/1200)^(-30*12))/(3/1200))

Cash Flow = 421.6

PVOrdinary Annuity = C*[(1-(1+i/100)^(-n))/(i/100)]

C = Cash flow per period

i = interest rate

n = number of payments

PV= 421.604*((1-(1+ 3/1200)^(-15*12))/(3/1200))

PV = 61050.57

Interest saved = monthly payments*number of payments left-PV of payments at 15 years

=421.604*15*12-61050.57=14838.15